Gallium alloys are promising materials in biomedical engineering, electronics, and wireless communications, thanks to their good conductivity and their ability to sustain large deformations. They can be transported in capillaries using continuous electrowetting (CEW). Current models of CEW-driven flows do not address the transient response to fast changes in the excitation voltage, crucial in many applications. Here, we study the CEW-driven oscillatory motion of a drop of a Gallium alloy inside a capillary. We consider inertia, viscosity and the transient response of the electrical circuit consisting of the drop plus the electrolyte where it is immersed. The theory describes fairly well the experimental drop velocity and explains the existence of an optimal frequency that maximizes the velocity.